Method for designing tire noise pitch sequence

ABSTRACT

A method of designing a pitch noise pitch sequence includes the steps of first defining the characteristics of the tire noise generated by tire tread lug stiffness variations and then defining a tire noise pitch sequence that yields the defined characteristics to provide preferred modulation characteristics and good level characteristics. A tire is provided having a pitch sequence designed from this method. The tire has five different pitches with pitch ratios of 1.00, 1.10, 1.25, 1.4, and 1.50.

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims priority from U.S. Provisional PatentApplication serial No. 60/423,094 filed Nov. 1, 2002; the disclosure ofwhich are incorporated herein by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Technical Field

[0003] The present invention generally relates to methods of designingtread patterns for tire noise. More particularly, the invention relatesto a method for designing tread pattern tire noise pitch sequences bypre-selecting variations in lug stiffness characteristics. The inventionspecifically relates to a method for designing tire noise pitchsequences to achieve preferred characteristics of variations in treadlug stiffness based on the distribution of the lugs in the tire noisepitch sequence.

[0004] 2. Background Information

[0005] One aspect of tire design involves minimizing undesirable tirenoise. Tire noise is generated when the lugs of the tread patterncontact the road surface. An unvarying tread pattern, or mono pitchtread pattern, creates an undesirable tonal, or mono pitch sound. Tiredesigners vary the tread pattern to avoid mono pitch sounds. The treadpatterns are typically varied by altering the size of the tread pitchesaround the circumference of the tire. Varying the sizes of the treadpitches tends to reduce mono pitch tire noise by broadening thefrequency domain of the noise spectrum but undesirable noise in the timedomain can still be created.

[0006] Tread patterns are currently analyzed by comparing the tire noisegenerated by different variations in the tread pitches. Known analysistechniques allow the tire designer to select a pitch pattern for thetread design that generates acceptable tire noise. One such techniqueuses the Fourier spectrum of the pitch sequence to identifyobjectionable pitch sequences. Another technique disclosed in U.S. Pat.No. 6,112,167 analyzes portions of the pitch sequence around thecircumference of the tire. Although these techniques have beeneffective, tire designers have found that known techniques can result intire noise pitch sequence designs that pass initial screening whilestill having undesirable tire noise. Tire molds having such sequencesmust be rebuilt or modified to reduce the undesirable noise. One causeof undesirable noise is tire noise attributed to the variations in thelug stiffness around the circumference of the tire.

[0007] When the size of the tread pitches is varied, the size of thelugs of the tread pattern is varied. The lugs thus have differentstiffnesses and produce different sound amplitudes when they contact theroad surface. These differences create sound amplitude variation thatcan make an otherwise desirable pitch sequence undesirable. In the past,this undesirable tire noise was not analyzed and tires would be producedbefore the undesirable noise was recognized. If the customer objected tothe noise, the tire manufacturer would have to scrap the expensive tiremold or would have to modify the mold. In response to this issue, theart thus desired a secondary screening method that allows the tiredesigner to compare a group of otherwise desirable pitch sequences. Thisscreening technique is disclosed in pending patent application US2003/0040886 A1 dated Feb. 27, 2003, which describes a method forcomparing tread designs based on tire noise generated by tire tread lugstiffness variation. The art thus desires a method to develop treaddesigns with pre-selected lug stiffness variation characteristics. Sucha tread pattern design method would define tire noise pitch sequencesfor optimized lug stiffness variations and tire noise levelcharacteristics. FIGS. 1A-C and 2A-C demonstrate the inherentdifficulties in defining tire noise pitch sequences with optimized lugstiffness variations and tire noise level characteristics. FIGS. 1A-Cprovide for a 60-pitch noise sequence with good level characteristics,but poor lug stiffness (further referred to as modulation)characteristics. Good level characteristics consist of a smooth spectrumabout the first tread passage harmonic range that is centered at 60harmonics for 60 pitches. Notice that for the sequence depicted in FIG.1C, there is relatively high modulation levels at the first and secondmodulation order. These high levels would translate to a tire treadpattern with a strong once and twice per revolution noise variation. Atire pattern with good modulation characteristics would have lowmodulation levels. FIGS. 2A-C demonstrate a tire noise pitch sequencewith good modulation characteristics. An analysis of the harmoniccontent of this sequence provides for a narrow, tonal band of energyabout the 60^(th), 120^(th), 180^(th) harmonic and subsequent multiplesof 60 harmonics with high, undesirable, level characteristics.

SUMMARY OF THE INVENTION

[0008] In view of the foregoing, the present invention provides a methodof defining tire noise pitch sequences based on preferredcharacteristics of the tire noise generated by tire tread lug stiffnessvariations. The method of the invention may be used to provide a tirenoise pitch sequence with preferred modulation characteristics and goodlevel characteristics.

[0009] The invention provides a method including the steps of definingthe amplitudes of the modulation orders; defining the phases for eachorder; summing the functions for each order; and defining the tire noisepitch sequence from the summation of the functions.

[0010] The invention also provides a tire having a pitch sequencedesigned from the method of the invention. In one embodiment, theinvention provides a tire having a body having a tread that has a pitchsequence; and the pitch sequence having five different size pitches withpitch ratios of 1.00, 1.10, 1.25, 1.4, and 1.50.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011]FIG. 1A is a graph showing the harmonic analysis result for a tirewith a good harmonic spectrum; the X axis being the harmonic spectrum ofevent occurrences per tire revolution and the Y axis being theamplitude.

[0012]FIG. 1B is a graph showing the modulation analysis result for atire with bad modulation orders; the X axis being the modulation orderand the Y axis being the amplitude.

[0013]FIG. 1C is the pitch sequence analyzed in FIGS. 1A and 1B with thepitch ratios listed at the end of the pitch sequence.

[0014]FIG. 2A is a graph showing the harmonic analysis result for a tirewith a bad harmonic spectrum; the X axis being the harmonic spectrum ofevent occurrences per tire revolution and the Y axis being theamplitude.

[0015]FIG. 2B is a graph showing the modulation analysis result for atire with good modulation orders; the X axis being the modulation orderand the Y axis being the amplitude.

[0016]FIG. 2C is the pitch sequence analyzed in FIGS. 2A and 2B with thepitch ratios listed at the end of the pitch sequence.

[0017]FIG. 3 is a graph showing a series of seven cosine functions withzero phase and equal amplitude; the X axis being degrees from a setpoint on a tire and the Y axes being amplitudes.

[0018]FIG. 4 is a graph showing the Y function for the seven signals ofFIG. 3; the X axis being degrees from a set point on a tire and the Yaxis being amplitude.

[0019]FIG. 5 is a graph showing the series of functions from Table 2,Set 1; the X axis being degrees from a set point on a tire and the Yaxis being amplitude.

[0020]FIG. 6 is the Y function for the functions of FIG. 5; the X axisbeing degrees from a set point on a tire and the Y axis being amplitude.

[0021]FIG. 7 is a graph showing the series of functions from Table 2,Set 2; the X axis being degrees from a set point on a tire and the Yaxis being amplitude.

[0022]FIG. 8 is the Y function for the functions of FIG. 7; the X axisbeing degrees from a set point on a tire and the Y axis being amplitude.

[0023]FIG. 9A is a graph showing the harmonic analysis result of thepitch sequence designed from the curve of FIG. 6; the X axis being theharmonic response and the Y axis being the amplitude.

[0024]FIG. 9B is a graph showing the modulation analysis result of thepitch sequence designed from the curve of FIG. 6; the X axis being themodulation orders and the Y axis being the amplitude.

[0025]FIG. 9C is a graph showing the pitch sequence designed from thecurve of FIG. 6; the X axis being the pitch number and the Y axis beingthe pitch size.

[0026]FIG. 9D is a graph showing the comparison between the targetdesign curve and the actual curve obtained from the designed pitchsequence; the X axis being location in degrees and the Y axis being theamplitude.

[0027]FIG. 10A is a graph showing the harmonic analysis result of thepitch sequence designed from the curve of FIG. 8; the X axis being theharmonic response and the Y axis being the amplitude.

[0028]FIG. 10B is a graph showing the modulation analysis result of thepitch sequence designed from the curve of FIG. 8; the X axis being themodulation orders and the Y axis being the amplitude.

[0029]FIG. 10C is a graph showing the pitch sequence designed from thecurve of FIG. 8; the X axis being the pitch number and the Y axis beingthe pitch size.

[0030]FIG. 10D is a graph showing the comparison between the targetdesign curve and the actual curve obtained from the designed pitchsequence; the X axis being location in degrees and the Y axis being theamplitude.

[0031]FIG. 11 is a flow chart showing a method for creating andcomparing tire noise pitch sequences.

[0032]FIG. 12 shows the relationship between FIGS. 12A and 12B andshowing exemplary pitch sequences for 53-67 pitch designs.

[0033]FIGS. 12A and 12B are a chart of exemplary pitch sequencesdesigned in accordance with the present invention (FIG. 12B is acontinuation of FIG. 12A).

[0034]FIG. 13 shows the relationship between FIGS. 13A and 13B andshowing exemplary pitch sequences for 68-80 pitch designs.

[0035]FIGS. 13A and 13B are a chart of exemplary pitch sequencesdesigned in accordance with the present invention (FIG. 12B is acontinuation of FIG. 12A).

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0036] The first part of the method is to define the preferredmodulation characteristics and to build a function based on the combinedmodulation characteristics. It is generally known in the art that afirst or second order is undesirable. Lug stiffness variations of thefirst order can magnify any imbalance or out of round in the tirerelating to uniformity performance. As the order increases the effect onuniformity is diminished. Thus it is preferred to minimize the first twomodulation orders. It is not prudent, though, to minimize all of themodulation orders, because the only way to have a noise treatmentwithout modulation, is one in which all of the pitch sizes are the same.This type of sequence, commonly referred to as a mono pitch, produces aconstant tone or mono pitch sound, which is also undesirable. Thus, itis desired to have some modulation in each of the orders 3 and above. Itis desirable to have a smooth transition of the modulation orders. Thenumber of modulation orders and the levels selected can vary. It hasbeen found that it is not necessary to analyze modulation orders higherthan seven because they generally approach zero and the analysis ofthese orders consumes too much processing time compared to the benefitreceived from the analysis.

[0037] In order to show an example of the invention, the data shown inTable 1 is analyzed in the following description. Table 1 lists thepre-selected levels for the selected modulation orders. Although thelevels for the first and second orders preferably are selected to bezero in the exemplary embodiment, values other than zero may be usedwith the method of the present invention as long as these values areminimized with respect to the remaining orders. It is also desirable toset the value of the third order to be less than the values of thefourth and fifth orders. As noted abover, all of the values cannot beset to zero because a monopitch would be the result. The levels shouldbe set high enough to avoid a monopitch while low enough to avoidundesirable tones. The individual level can range from as little as 0 toas much as 20. The preferred embodiment sets a preferable range ofbetween 1 to 5 for modulation orders above and including 3. The numbersin Table 1 meet these limitations and provide a smooth transitionbetween different orders. TABLE 1 Order Level 1 0 2 0 3 1.5 4 2.2 5 2.256 2 7 1.5

[0038] After the levels for the modulation orders have been defined, acomplex wave is created by a summation of cosine waves with pre-selectedamplitude and phase characteristics. Equation 1 is the Fourier seriesexpansion of the cosine functions.$Y = {\sum\limits_{k = 1}^{n}\quad {A_{k}{\cos ( {{k \cdot \theta} + \phi_{k}} )}}}$

[0039] . . . where Y is the resultant function, A_(k) are the amplitudesof each k^(th) order, theta is the angle from 1 to 360 degrees andphi_(k) is the phase angle of the k^(th) order.

[0040]FIG. 3 graphically shows a series of 7 cosine functions with zerophase and equal amplitude. FIG. 4 shows the function, Y, for the 7signals of FIG. 3.

[0041] By building a series of Y functions for a set of pre-definedA_(k) as defined in table 1, noise sequences can be defined by randomly,or in an orderly manner, defining the phase angles, f_(k), for eachorder. The phase angles may be defined in an orderly manner by loopingthrough the potential phases at a fixed increment such as 1 degree.Table 2 shows two sets of phases. The first set has all of themodulation orders in phase and the second set has orders 4 through 7with varying phase. TABLE 2 Phase Angles in Degrees Set 1 Set 2 OrderLevel In Phase Phased 1 0  0*  0* 2 0  0*  0* 3 1.5  0**  0** 4 2.2 097  5 2.25 0 −73  6 2 0 −105    7 1.5 0 4

[0042]FIGS. 5, 6, 7 and 8 represent the waves for each curve withspecified phase as well as the resultant wave shape, which is arepresentation of the lug stiffness variation of some tire noisetreatment. A computer may be used to generate a large number ofmodulation characteristics including different amplitudes and phaseangles. A computer program may be used to create a wide variety ofresultant waves shapes that are then used to design a wide variety ofpitch sequences that are then compared to obtain desirable pitchsequences.

[0043] The second part of the method constructs a tire noise pitchsequence where the calculation of the lug stiffness variation curvematches, as closely as possible, the resultant wave shape. The shape ofthe lug stiffness variation curve D, as discussed in prior art(publication no. US 2003/0040886 A1 dated Feb. 27, 2003), is defined asthe accumulation of the deviation of the arc length from the arc lengthof the mean pitch size. D is a vector of the difference in the actualarc length from a fixed arbitrary reference point to the end of thei^(th) pitch size.

D={D₁, D₂, D₃, . . . , D_(i), . . . D_(N−1), D_(N)}

[0044] N is the total number of tread pitches placed about thecircumference of the tire. D_(i) can be calculated using the followingrelationship: $\begin{matrix}{D_{i} = {X_{i} - {\overset{\_}{X}}_{i}}} \\{X_{i} = {\sum\limits_{j = 1}^{i}\quad L_{j}}} \\{{\overset{\_}{X}}_{i} = {i \times \frac{C}{N}}}\end{matrix}$

[0045] wherein:

[0046] X_(i) is the arc length from the fixed reference point to the endof the i^(th) tread pitch.

[0047] {overscore (x)}_(i) is the arc length of i pitches times the meanpitch size.

[0048] L_(j) is the pitch length of the j^(th) tread pitch.

[0049] C is the tire circumference in degrees=360 degrees.

[0050] N is the number of tire tread pitches.

[0051] Y is a function of circumferential angle, theta. Y_(i) can bedefined as the target curve, Y, evaluated at the at i times thecircumference, C, divided by the number of pitches, N.$Y_{i} = {Y_{\theta = {i \times \frac{C}{N}}}}$

[0052] D_(i), the design curve shape at i is an approximation of Y_(i).$\begin{matrix}{Y_{i} \cong D_{i}} \\{Y_{i} \cong {{\sum\limits_{j = 1}^{i}\quad L_{j}} - {i \times \frac{C}{N}}}} \\{{\sum\limits_{j = 1}^{i}\quad L_{j}} \cong {Y_{i} + {i \times \frac{C}{N}}}}\end{matrix}$

[0053] Once the desired number or tread pitches, N, each pitch lengthcan then found in sequential order. For reference in this example N=60,although N can range from as low as 20 to as high as 100 total pitches.The first size is found by solving the equation for i=1 with N=60 &C=360. $\begin{matrix}{{\sum\limits_{j = 1}^{1}\quad L_{j}} = {Y_{1} + {1 \times \frac{360}{60}}}} \\{L_{1} = {Y_{1} + 60}}\end{matrix}$

[0054] The second size is found in the same manner as the first whileutilizing L₁. $\begin{matrix}{{\sum\limits_{j = 1}^{2}\quad L_{j}} = {Y_{2} + {2 \times \frac{360}{60}}}} \\{{L_{1} + L_{2}} = {Y_{2} + 120}} \\{L_{2} = {Y_{2} + 120 - L_{1}}} \\{L_{2} = {Y_{2} + 120 - ( {Y_{1} + 60} )}} \\{L_{2} = {( {Y_{2} - Y_{1}} ) + 60}}\end{matrix}$

[0055] The general form of the solution of the L_(i)array is as follows.$\begin{matrix}{L_{i = 1} = {Y_{i} + \frac{C}{N}}} \\{L_{i \geq 2} = {Y_{i} - {\sum\limits_{j = 1}^{i - 1}\quad Y_{j}} + \frac{C}{N}}}\end{matrix}$

[0056] This process will define a unique set of pitch sizes, L_(i),which will give the specified lug stiffness variation characteristics.L_(i) will yield N unique pitch lengths. N unique tire tread pitchlengths, while desired by the tire noise pitch sequence designer, isimpractical when considering the design of a tire mold. The higher thenumber of unique pitch lengths, the higher the complexity and costassociated with the production of the tire mold. The art typically usesas few as 2 to as many as 10 unique pitch sizes in order to decrease thecomplexity of the mold making process. If desired, a larger number ofpitch sizes may be used.

[0057] The third part of the method involves converting from N uniquepitch sizes to M prescribed pitch sizes. A numeric value is selectedthat defines the ratio between the largest pitch size to the smallestpitch size (the pitch ratio). This pitch ratio typically ranges from 1.2to 1.8, but other ratios are not outside the embodiment of this method.For the purposes of continuing the example of N=60, M is chosen as 3 andthe pitch ratio, P, is set at 1.5. The three sizes, designated as 1, 2,and 3 have the internal pitch ratios of 1.00, 1.25, and 1.50respectively. The N unique pitch sizes are then fit to the M selectedsizes. For example, if N ranges from 3.5 degrees to 6.5 degrees, size 1may be set to include all N sizes from 3.5 degrees to 4.5 degrees; size2 may be set to include all N sizes from 4.5 degrees to 5.5 degrees; andsize 3 may be set to include all N sizes from 5.5 degrees to 6.5degrees. If this example, size 1 may be 4 degrees, size 2 may be 5degrees, and size 3 may be 6 degrees. The pitch ratio is 6/4 or 1.5.

[0058]FIGS. 9 and 10 show the two pitch sequences for N=60, M=3, andP=1.5 for the two resultant wave curves from FIGS. 6 and 8 respectivelythat contain the amplitude and phase information from table 2.

[0059] As can be seen, the actual response function, bottom set ofcurves in FIGS. 9 and 10, is set to match as closely as possible, thedesign response function. Additionally, as can be seen, the actual setof modulation order amplitudes has the basic features for goodmodulation performance. The reason the actual modulation amplitudes andthe design modulation amplitudes vary is the selection of M=3 designsizes rather than N unique design sizes.

[0060] Another pitch design that has been found to be particularlyuseful with the method of the present invention is a pitch design havingfive different pitch sizes defined by the pitch ratios of 1.00 (smallestpitch length), 1.10, 1.25, 1.4, and 1.5 (largest pitch length). Thistype of pitch design has been found to be useful for creating pitchsequences having between 53 and 80 pitches. Exemplary pitch sequencesthat have been designed using the method of the present invention andthis pitch design include the following pitch sequences for 53 pitch, 68pitch, and 80 pitch sequences.

[0061] 53 pitch

[0062] 32111233444333323344321113455421113444322233322234555

[0063] 68 pitch

[0064] 44443322211223455554311112345543222233433322334554322111233

[0065] 80 pitch

[0066]332111233444332222334555443221111223344554433211112345554332

[0067] These pitch sequences have been found to have prescribedmodulation (as defined by the method described above) and controlledhigher harmonics. Additional examples are shown in FIGS. 12 and 13.

[0068] The fourth part of the model involves selecting a tire noisetreatment. The tire noise treatment can be selected in any number ofways used by one skilled in the art. Preferably, for a tire noisetreatment to be acceptable it should have good level characteristics. Acomparison of the two tire noise treatments, A and B, from FIGS. 9 and10 respectively, provides that the modulation performance of designs Aand B are similar, but design A has a narrow band with high amplitudeand is therefore undesirable. Design B has both good level and amplitudecharacteristics and therefore would be a candidate to be used in adesign. Design B thus provides a tire noise pitch sequence that has bothgood modulation and good level characteristics. In past design methods,the art recognized bad modulation as a byproduct of a design with goodlevel characteristics. The method described above allows the designer tocreate tire noise pitch sequences having good performance for bothmodulation and level.

[0069]FIG. 11 shows a method for creating and comparing tire noise pitchsequences. Block 1 is the step of defining the amplitudes of themodulation orders. Block 2 is the step of prescribing the phases (eitherorderly or randomly). Block 3 is the step of prescribing the number ofpitches, the number of unique pitch sizes, and the pitch size ratios.Block 4 is the step of defining the tire noise pitch sequence andanalyzing its performance. Block 5 is the step of determining the tirenoise pitch sequence is optimized. If the answer is no, the user goesback to Block 1. If the answer is yes, the user proceeds to Block 6where the pitch sequence is stored for use on a tire. This method allowsthe user to create a catalog of acceptable pitch sequences that may beused on future tires.

[0070] In the foregoing description, certain terms have been used forbrevity, clearness, and understanding. No unnecessary limitations are tobe implied therefrom beyond the requirement of the prior art becausesuch terms are used for descriptive purposes and are intended to bebroadly construed.

[0071] Moreover, the description and illustration of the invention is anexample and the invention is not limited to the exact details shown ordescribed.

1. A method for designing a tire noise pitch sequence for a pneumatictire; the method comprising the steps of: selecting a number ofmodulation orders; defining the amplitudes of the modulation orders;defining the phases for each modulation order; creating a function foreach modulation order that includes the defined amplitudes and phases;summing the functions that define the modulation orders; and definingthe tire noise pitch sequence from the summation of the functions. 2.The method of claim 1, wherein the step of defining the tire noise pitchsequence includes the step of calculating a determined number of pitchsizes from the summation of the functions.
 3. The method of claim 2,wherein the step of calculating the determined number of pitch sizesfrom the summation of the functions includes the step of using theaccumulation of the deviation of the arc length from the arc length ofthe mean pitch size.
 4. The method of claim 3, further comprising thestep of interpolating a curve defined by the accumulation of thedeviation of the arc length from the arc length of the mean pitch size.5. The method of claim 4, further comprising the steps of: selecting thetotal number of pitches, the number of different pitch sizes, and thepitch ratios; and fitting the determined number of pitch sizes to theselected number of pitch sizes.
 6. The method of claim 2, furthercomprising the steps of: selecting the total number of pitches, thenumber of different pitch sizes, and the pitch ratios; and fitting thedetermined number of pitch sizes to the selected number of pitch sizes.7. The method of claim 6, further comprising the step of setting theselected number of pitch sizes to a number between 3 and
 7. 8. Themethod of claim 6, wherein the step of fitting the determined number ofpitch sizes to the selected number of pitch sizes includes the step ofidentifying the range of determined number of pitch sizes and evenlydividing the identified range by the selected number of pitch sizes. 9.The method of claim 6, further comprising the steps of selecting thenumber of different pitch sizes to be 5 and selecting the pitch ratiosto be 1.00, 1.10, 1.25, 1.40, and 1.50.
 10. The method of claim 6,further comprising the steps of selecting the number of different pitchsizes to be 3 and selecting the pitch ratios to be 1.00, 1.25, and 1.50.11. The method of claim 1, wherein the step of selecting the number ofmodulation orders includes the step of selecting between 3 and 7modulation orders.
 12. The method of claim 11, wherein the step ofdefining the amplitudes of the modulation orders includes the step ofdefining the amplitudes of the first and second orders to be smallerthan the amplitudes of the remaining orders.
 13. The method of claim 12,wherein the step of defining the amplitudes of the modulation ordersincludes the step of defining the amplitudes of the first and secondorders to be zero.
 14. The method of claim 12, wherein the step ofdefining the amplitudes of the modulation orders includes the step ofvarying the amplitudes for the selected modulation orders.
 15. A methodfor defining a tire noise pitch sequences; comprising the steps of: (a)first defining the characteristics of the tire noise generated by tiretread lug stiffness variations; and (b) then defining a tire noise pitchsequence that yields the defined characteristics to provide preferredmodulation characteristics and good level characteristics.
 16. Themethod of claim 15, wherein step (a) includes the steps of: defining theamplitudes of at least five modulation orders; defining the phases foreach modulation order; creating a function for each modulation orderthat includes the defined amplitudes and phases; and summing thefunctions that define the modulation orders to create a complex wave Y.17. The method of claim 16, further comprising the steps of: defining alug stiffness variation curve (Di) to be the accumulation of thedeviation of the arc length from the arc length of the mean pitch size;setting the lug stiffness variation curve equal to the Y curve; andsolving the equation to obtain a unique set of pitch sizes.
 18. Themethod of claim 17, further comprising the steps of selecting the totalnumber of pitches, the number of different pitch sizes, and the pitchratios; and fitting the unique set of pitch sizes to the selected numberof pitch sizes.
 19. A tire comprising: a body having a tread that has apitch sequence; and the pitch sequence having five different sizepitches with pitch ratios of 1.00, 1.10, 1.25, 1.4, and 1.50.
 20. Thetire of claim 19, wherein the pitch sequence includes 53 to 80 pitches.